Blow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem
Analysis of PDEs
2011-02-25 v2 Mathematical Physics
math.MP
Abstract
We consider the energy critical Schrodinger map to the 2-sphere for equivariant initial data of homotopy number k=1. We show the existence of a set of smooth initial data arbitrarily close to the ground state harmonic map in the scale invariant norm which generates finite time blow up solutions. We give a sharp description of the corresponding singularity formation which occurs by concentration of a universal bubble of energy. The concentration rate is given by for some . The detailed proofs of the results will appear in a companion paper.
Cite
@article{arxiv.1102.4308,
title = {Blow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem},
author = {Frank Merle and Pierre Raphael and Igor Rodnianski},
journal= {arXiv preprint arXiv:1102.4308},
year = {2011}
}
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